ML20241A065

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Seminar 4 - Advanced Methods Power Point
ML20241A065
Person / Time
Issue date: 08/28/2020
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Office of Nuclear Regulatory Research
To:
M. Homiack
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Download: ML20241A065 (54)
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1 EVENTS

1. Models Overview June 3rd l 10-12 EDT
2. Setting Up the Inputs July 15th l 10-12 EDT
3. Running the Simulation and Retrieving Results July 29th l 10-12 EDT
4. Advanced Methods August 5th l 10-12 EDT 2

Seminar 4: Advanced Methods Agenda Introduction and Opening Remarks Inputs - Advanced Methods Sampling - Advanced Methods Results and Outputs - Advanced Methods Improving Efficiency Questions and Answers Closing Remarks 3

PRIOR WEBINARS

  • Recordings of the Extremely Low Probability of Rupture (xLPR) webinars are, or will soon be, available on YouTube.com

- Public Release https://www.youtube.com/watch?v=McVVFriy7wQ

- Seminar 1: Models Overview https://www.youtube.com/watch?v=vsOOtdXYxoY&

- Seminar 2: Setting up the Inputs https://youtu.be/nRk5VBAT8ww

- Seminar 3: Running the Simulation and Retrieving Results

- Seminar 4: Advanced Methods

  • Search for xLPR on YouTube.com, or go to the U.S.

Nuclear Regulatory Commission (NRC)s YouTube Channel (https://www.youtube.com/user/NRCgov) 4

WEBEX Q+A Webex Internet Browser Webex Desktop Client 5

REFERENCES

  • xLPR-GR-FW, Computational Framework Development, Testing, and Analysis, Version 1.0, January 2020.*
  • xLPR-UM-2.1, User Manual for xLPR Version 2.1, Version 1.0, May 2020.
  • To be released at a later date 6

Inputs Advanced Methods

ENTERING LOG-NORMAL DISTRIBUTIONS

  • In xLPR Version 2.1 (V2.1), the log- (mean of log-transformed data) and normal distribution may be based (standard deviation of log-on either the true (arithmetic) mean and standard deviation, or the transformed data) are the traditional geometric mean and geometric parameters of the log-normal standard deviation distribution

- True (arithmetic) mean (= )

- True (arithmetic) standard deviation

(= 1 )

- Geometric mean (= )

- Geometric standard deviation (

8

CORRELATED VARIABLES

  • Correlation is applied pairwise for select pairs of inputs

- Applies to certain inputs on the Properties and material (i.e.,

Left Pipe, Right Pipe, Weld, and Mitigation) tabs of the Input Set

- Applied as a rank correlation

  • Strength of correlation is input by the user

- Correlation coefficient between -1 and 1 9

DETERMINING IF INPUTS ARE OUTSIDE RANGE OF APPLICABILITY (1/2)

  • Automated checks are included within the Input Set

- Allowable input range is shown in left-most column

- Values out of allowable range are highlighted in red

  • Sim Editor performs the same allowable input range checks as the input set

- Demonstrated in the Setting Up the Inputs seminar 10

DETERMINING IF INPUTS ARE OUTSIDE RANGE OF APPLICABILITY (2/2)

  • xLPR-UM-2.1, Appendix E, includes module-specific input limits

- Physical limits /

range of validity

  • Module subgroup reports* include additional details on range of validation for each module *To be released at a later date 11

TOOLS FOR COMPARING INPUT SETS

- Included with some Microsoft Office licenses

- Application is separate from Excel

  • Conditional Formatting or Boolean logic in Excel
  • Many other options 12

Sampling Advanced Methods

SAMPLING

  • There are many ways to sample inputs in xLPR V2.1 for uncertainty propagation:

- Simple Random Sampling (SRS)

- Latin Hypercube Sampling (LHS)

- Importance Sampling

- Discrete Probability Distribution (DPD)

  • Can be used with LHS or SRS 14

CHOOSING A SAMPLING SCHEME

  • SRS is simplest - easy to analyze, combine results across runs, and calculate sampling uncertainty
  • LHS is an improvement on simple random sampling without increasing the computation time or complexity of post-processing
  • Importance sampling helps estimate very small probabilities in reasonable computing times

- Chosen after preliminary sensitivity analyses have been conducted

  • DPD results in samples that are always uniformly distributed over the sample space, but take on fewer unique values

- 15 Can be useful when simulation sample size is limited. However, li t i l ti tb dt i ti t i

SIMPLE RANDOM SAMPLING

  • The simplest Monte Carlo sampling scheme is SRS

- All inputs are randomly sampled from their input distributions

- Pros: Easy to implement, easy to explain, and easy to analyze data

- Cons: Sufficiently large samples may not be possible to achieve reasonably low sampling uncertainty 16

LATIN HYPERCUBE SAMPLING

  • Force samples to be spread across domain of the input distributions using dense stratification across range of each variable
  • Pros: Lower sampling uncertainty than SRS, easy to analyze
  • Cons: Difficult to estimate sampling uncertainty SAND2001-0417 17

SWITCHING BETWEEN SIMPLE RANDOM AND LATIN HYPERCUBE SAMPLING

  • Epistemic (outer) loop
  • Aleatory (inner) loop

- Run -> Simulation - From model root, Settings -> Monte right-click Carlo Main_Model -Monte

- Set up epistemic Carlo sample size and - Set up aleatory random seed -> random seed ->

Monte Carlo Monte Carlo 18

IMPORTANCE SAMPLING (1/3)

  • Over-sample important parts of the input space
  • Pros: Better estimation of rare event probabilities
  • Cons: Harder to implement, more difficult to analyze data, poor implementation can increase sampling uncertainty 19

IMPORTANCE SAMPLING (2/3)

  • Applying importance sampling in xLPR V2.1

- User has to select whether to apply importance sampling on each variable

- Importance sampling concentrates half of the samples taken for a given input within a region about a user-selected quantile

  • Width of this region depends on the number of inputs selected for importance sampling 20

IMPORTANCE SAMPLING (2/3) 21

DISCRETE PROBABILITY DISTRIBUTION

  • Discretizes the domain in as many equiprobable strata (or levels) as selected by the user
  • After partitioning the sample space, DPD uses the conditional mean of the stratum

- If 5 levels are defined, any quantile value in [0, 0.2] will be set to distribution mean over [0, 0.2], but not necessarily q=0.1

- Similarly for subsequent quantiles [0.2,0.4], [0.4,0.6],

  • When DPD is selected, discretization is applied to all variables within the loop (epistemic (outer) or aleatory (inner))

22

SINGLE-LOOP SIMULATIONS (1/2)

  • To sample all variables in the epistemic (outer) loop

- Set all sampled inputs to epistemic in the Input Set

- The submodel requires at least two realizations within the aleatory (inner) loop

  • Can adjust settings to run only one realization

- Run only one realization in the aleatory (inner) loop

  • Set up aleatory random seed

-> Monte Carlo

  • Epistemic (outer) loop allows for larger sample sizes using LHS 23

SINGLE-LOOP SIMULATIONS (2/2)

  • To sample all variables in the aleatory (inner) loop

- Set all sampled inputs to aleatory in the Input Set

- Use different random seed for new instance of parent model

  • Set up aleatory random seed

-> Monte Carlo

  • Aleatory (inner) loop allows for larger sample sizes using SRS 24

DETEMINISTIC SINGLE-REALIZATION SIMULATION

  • For a deterministic, single-realization run, run only one realization in both the epistemic (outer) and aleatory (inner) loops
  • Set all inputs to constant 25

Demo - Simulation Settings Questions?

xlpr@nrc.gov xlpr@epri.com for Additional Information

Results and Outputs Advanced Methods

INTERPRETING THE RUN LOG

  • The GoldSim environment creates a run log

- User should inspect the run log for warnings and error messages

- The Framework writes a message to the run log every time a module has an error

  • To open the run log:

- In GoldSim, click Run -> View Run Log

- Run log will be displayed in Notepad and saved as a text file (GoldSim Run Log.txt) 29

EXTRACTING RESULTS FROM GOLDSIM

  • By default, xLPR V2.1 does not export results to external files
  • The results from Time History result elements (located in the model root) can be exported to a specific Excel or text file

- Use the Export Results To pull down menu of the result elements 30

ADDING INTERMEDIATE OUTPUT VARIABLES (1/2)

  • Creating new result elements

- Only possible with GoldSim Pro

- Can view results of existing GoldSim elements with GoldSim Player

- Frequently used result elements include:

  • Time History Result
  • Distribution Result
  • Array result 31

ADDING INTERMEDIATE OUTPUT VARIABLES (2/2)

  • Getting results out of the main model

- Only possible with GoldSim Pro

  • The submodel has an interface to the model root (or epistemic (outer) loop)

- Right-click Main_Model ->

Properties -> Interface

- Additional output variables are added using green plus-sign 32

SCREENING RESULTS (1/3)

  • When running a large sample size, it may be difficult to extract all of the results
  • While GoldSim only displays the first 1,000 values, a screening feature allows other values to be seen

- See page 533 of the GoldSim User Manual, Volume 2, Version 11.1

  • Two ways to access screening settings:

- Go to Run -> Simulation Settings ->

Monte Carlo -> Result Options

- In result element, click on Edit Properties icon, then Monte Carlo Result Options 33

SCREENING RESULTS (2/3)

  • Screening is controlled under Realization Classification and Screening
  • By default, screening is set to All realizations
  • Additional conditions can be added and applied for screening

- Click on Add

- Enter a new condition

- Uncheck Category 1 (All realizations) 34

SCREENING RESULTS (3/3)

  • It is important to note:

- Conditions can also be used to screen out results (e.g., check Category 1 and uncheck Category 2)

- When screening is applied, the status of the file is changed to Result Mode (screened)

- Unchecking all categories may lead to GoldSim crashing. It is recommended to always save once a calculation is performed, before any screening.

- Multiple conditions can be applied, such as:

epistemic_realization>10 and epistemic_realization<31 35

SCREENING RESULTS EXAMPLE -

REALIZATIONS WITH INITIATED CRACKS (1/2)

  • Additional output is_cracked is added to Main Model interface

- Right-click Main_Model -> Properties -> Interface

- Additional output variables are added using green plus-sign 36

SCREENING RESULTS EXAMPLE -

REALIZATIONS WITH INITIATED CRACKS (2/2)

  • Insert a Data element that links to Main_Model.is_cracked

- Right click -> Insert Element ->

Inputs -> Data

  • Can then apply screening with the newly added output, is_cracked 37

POST-PROCESSING

  • After extracting results from GoldSim, can perform post-processing to calculate outputs not directly calculated in xLPR V2.1

- Examples

  • Leak-before-break ratio

- Ratio between critical crack size and crack size at detectable leakage

  • Time from detectable leakage to rupture

- Use tool of choice

  • Excel, R, Python, etc.

38

SENSITIVITY ANALYSIS

  • Sensitivity analysis is used to:

- Understand the relationship between model inputs and outputs

- Identify the inputs that have the most significant impact on the results of the model

  • Knowledge of the most important inputs can be used to:

- Target inputs where more information could be collected to decrease uncertainty

- Identify inputs for importance sampling to increase precision in estimating rare probabilities

  • Many statistical methodologies exist to determine which sampled inputs have the greatest influence on simulation outputs of interest

- Example:

Need toIn also savethe xLPR V2.1, allDirect sampled inputs Model 1 (DM1) multiplier is highly correlated with the probability of crack, while the hoop weld residual stress (WRS) pre-mitigation is not highly correlated with the probability of crack 39

Demo - Screening Results Questions?

xlpr@nrc.gov xlpr@epri.com for Additional Information

Improving Efficiency DISABLING OUTPUTS (1/2)

  • Many of the GoldSim elements have options to save time history or final values

- Can disable result elements in GoldSim Player

- Can edit settings using GoldSim Pro

  • When highlighting saved results, GoldSim shows saved variable names in bold text
  • Simulation settings and Main_Model properties show 43 saved result size

DISABLING OUTPUTS (2/2)

  • Several errors may occur if GoldSim memory limits are reached
  • Errors include, but are not limited to:

- Warning in Simulation Settings

- Errors occur (as shown on right)

- GoldSim crashes during run 44

TIME SETTINGS - SAVING FREQUENCY

  • GoldSim stores and saves the results of each realization
  • GoldSim provides the ability to estimate the final size of the model and adjust the output saving frequency to adjust the size of the results

- Main Model properties, Time tab 45

TIME SETTINGS - TIME STEP

  • In xLPR V2.1, the default time step is set to 1 month
  • This time step can be modified if needed, e.g., to investigate temporal convergence
  • The simulation time step can only be adjusted from the aleatory (inner) loop settings dashboard 46

DISTRIBUTED PROCESSING (1/4)

  • To run xLPR V2.1 in parallel (up to 4 slave processes), GoldSim Pro is required
  • GoldSim Distributed Processing Plus Module allows for more than 4 slave processes
  • First run the code with a small sample size to confirm all values from the Input Set have been updated

- While this should be done automatically, some issues have been found with input data not being updated when running xLPR V2.1 in parallel

  • Then, run in parallel on up to N-1 slave processes (per next slide)

- N = number of cores in the computers processor 47

DISTRIBUTED PROCESSING (2/4)

  • GoldSim Slave processes can be started using the Windows Run utility (Windows key + R)
  • Inside the Run utility, enter the following:

- "C:\Program Files (x86)\GTG\GoldSim 11.1\GoldSim.exe" -s

  • Each time this command is run, one slave process is started

- Repeat for as many slave processes that you would like to run 48

DISTRIBUTED PROCESSING (3/4)

  • User selects: Run -> Run on Network
  • Connect GoldSim master with slave processes

- For slave processes on the same computer, can use the localhost address

- Can click update status to confirm the link between the master and the slaves 49

DISTRIBUTED PROCESSING (4/4)

  • Parallel execution is only applied to the epistemic (outer) loop
  • Adjusting the number of realizations per slave transaction can improve runtimes

- Rule of thumb: 100 to 1,000 realizations per transaction

- Too small: requires more data transfer

- Too large: reduces benefits of parallel execution, longer times for data transfer

  • Press Run Simulation button to run xLPR V2.1 50

Demo - Distributed Processing Closing Remarks LOOKING FORWARD

  • Development of an xLPR user group is underway
  • Stay tuned for further communications

- Survey will be distributed to users 53

Questions?

xlpr@nrc.gov xlpr@epri.com for Additional Information

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